A Class of Multi-Output Extended Nonlinear Observable Normal Forms

Transforming a nonlinear dynamical system by adding auxiliary dynamics is one of the most recent tools to design an observer. While significant theoretical progress has been made in characterizing systems amenable to such transformationsthrough both geometric and analytical frameworks. However, one finds only a few examples on this topic. Therefore, this paper proposes a novel approach by introducing a change of coordinate transformations and a set of coupled auxiliary dynamics to transform a class of multi-output nonlinear dynamical systems into the extended observable normal forms. Specifically, this normal form enables the straightforward implementation of the well-established high-gain observer design framework. Furthermore, it is more comprehensible and easier of this process in practice that without use the calculation of the Lie brackets.